Transcendental #s

[collegebookworm]

On District 2, #19:

19. Which of the following is NOT a transcendental number?

(A) 1.6180339887... (B) 2.7182818285... (C) .3245324532...
(D) 3.1415926536... (E) 0.6180339887...

The correct answer is (C), since that value is the solution to 9999x - 3245 = 0.
Aren't the golden ratio [unparseable or potentially dangerous latex formula] (A) and its inverse [unparseable or potentially dangerous latex formula] (E) both NOT transcendental as well?

My equations were:
([unparseable or potentially dangerous latex formula]) [unparseable or potentially dangerous latex formula] for the positive square root, and
([unparseable or potentially dangerous latex formula]) [unparseable or potentially dangerous latex formula] for the positive square root

[AuSmith]

Uh huh...

[Kurt]

Yeah, all three are algebraic. When I took this test in practice, I chose the continued fraction since it seemed to be obviously what he wanted.

He might have been using this definition:
[unparseable or potentially dangerous latex formula] to validate [unparseable or potentially dangerous latex formula] as transcendental...although if a number is a root to any polynomial equation with integer coefficients, it is supposed to be algebraic..so I don't think he thought it all the way through. (That definition above can easily be rewritten as the polynomial equation by expanding the hyperbolic sine function using its definition.)

[ZachB]

The golen ration is an algebraic irrational number, but not transcendental.

[AuSmith]

It's likely that he just wanted to change from irrational to transcendental and didn't get to change the choices... (why we need editors?)